Shagun invested Rs.30,000 at compound interest of 40% per annum, compounded semi- annually. If she received Rs. 4x after 24 months, then what is the value of 1.5x (in Rs.)?

Correct option is D

Given:

Principal (P) = Rs. 30,000
Rate of interest (R) = 40% per annum, compounded semi-annually
Time (T) = 24 months = 2 years
Amount received after 24 months = Rs. 4x

Formula Used:

In this case, since the interest is compounded semi-annually, n = 2, and the rate per period is R/2.
Thus, the formula becomes: $$A = P (1 +\frac{ R }{200})^{(2t)}$$​​

Solution:

Substituting the given values into the compound interest formula:

​$$A = 30,000 (1 + \frac{40}{200})^{(2 × 2)} \\\ \\A = 30,000 (1 + 0.2)^4\\\ \\A = 30,000 × (1.2)^4\\\ \\A = 30,000 × 2.0736 = 62,208$$​​
Since the amount received is Rs. 4x:
4x = 62,208
x = 62,208 / 4 = 15,552
To find 1.5x:
1.5x = 1.5 × 15,552 = 23,328
Thus, the value of 1.5x is Rs. 23,328.